Fundamentals and Analytical Applications of Multiway Calibration (eBook)

Graciela M. Escandar, Hector C. Goicoechea, Alejandro C Olivieri, Arsenio Munoz de la Pena (Herausgeber)

eBook Download: PDF | EPUB

2015 | 1. Auflage
618 Seiten
Elsevier Science (Verlag)
978-0-444-63537-2 (ISBN)

Infos

Fundamentals and Analytical Applications of Multi-Way Calibration presents researchers with a set of effective tools they can use to obtain the maximum information from instrumental data. It includes the most advanced techniques, methods, and algorithms related to multi-way calibration and the ways they can be applied to solve actual analytical problems.

This book provides a comprehensive coverage of the main aspects of multi-way analysis, including fundamentals and selected applications of chemometrics that can resolve complex analytical chemistry problems through the use of multi-way calibration.

• Includes the most advanced techniques, methods, and algorithms related to multi-way calibration and the ways they can be applied to solve actual analytical problems
• Presents researchers with a set of effective tools they can use to obtain the maximum information from instrumental data
• Provides comprehensive coverage of the main aspects of multi-way analysis, including fundamentals and selected applications of chemometrics

Textauszug

Views on Multiway Calibration

Its Past and Future

Nicolaas (Klaas) M. Faber    Chemometry Consultancy, Beek-Ubbergen, The Netherlands

The statistics-based methodology known as multiway calibration must appear like a fabled animal to the average practical analytical chemist. Fortunately, at its core this methodology amounts to estimating a calibration factor or sensitivity, essentially comparable to the slope of a straight-line fit, as detailed in the chapter on figures of merit. Let us therefore have a look at the natural progression of data complexity (Figure 1).

Figure 1 Schematic view of the data measured for a single chemical sample.

Univariate calibration, which is best exemplified by the familiar straight-line fit, commonly estimated using least-squares techniques, occupies a central place in the statistical part of an analytical chemist's curriculum. Univariate calibration works with scalars (plain single numbers) per sample and no index is required to mathematically characterize the data (it would always have the same value and therefore be noninformative). The analytical chemist should be comfortable here because the calibration methods and their results are as transparent as intuitive. I repeat: the calibration factor is the slope of the fitted line. How simple can it be to map signal space to concentration space?

Multivariate calibration, which digests vectors of data for each sample, already has a relatively high black-box character to the practical analytical chemist. What is the signal space? It is well known that if the data contain more than two elements, visualization is no longer straightforward, although technical escapes such as principal component analysis can be very useful. It is therefore not a surprise that the black-box character never fully disappeared since the introduction of calibration methods such as principal component regression and partial least squares (PLS) during the 1970s! Do these methods constitute black boxes to the seasoned chemometrician? Not that I know of and therefore this discrepancy constitutes a serious issue to pay attention to. There lie opportunities!

Multiway data require more than a single index. In the special case of two indices, the block of data is a mathematical matrix. Beyond that complexity, one refers to arrays. Here, I maintain the traditional distinction between multivariate and multiway calibration. Multiway data are also multivariate, but keeping the distinction is informative. It for example turns out that moving to multiway data leads to a real explosion of calibration methods. How is a practical analytical chemist going to find order in this obvious chaos? On his/her own? I conjecture: by learning from history. The problematic practical implementation of multivariate calibration methods led to fascinating opportunities for cross-fertilization between analytical chemists and chemometricians, and, from the increasing complexity of the data, I must infer that the opportunities for cross-fertilization must be even better for multiway calibration.

The analytical chemist is trained to know the mechanisms (e.g., chromatography, spectroscopy) leading to these highly complex data structures very well, whereas chemometricians are trained to even successfully work with rather “soft” data, about which little can be assumed. This appears to me as an important observation: chemometricians feel comfortable because they understand the methods to do the number crunching, while their understanding of the data might be at the same time “suboptimal” at best. Until now, however, for multiway calibration, even chemometricians need to construct their understanding about multiway calibration methods, when applied to analytical chemistry from what is scattered among “the literature.” This situation leads to needless artificial differences in opinion among chemometricians. I can therefore think of two reasons why this volume is timely and relatable. First, the field has obviously matured so that analytical chemists must begin to recognize the full potential of the methodology applicable to their data. Second, this volume may contribute to a harmonization regarding some needless differing insights among chemometricians!

So far the admittedly long introduction to the real introduction! How did it all start in analytical chemistry? It is well known that the initial idea behind the most powerful model for multiway data, known as PARAFAC, was proposed in 1944 by the extremely influential psychologist Raymond Cattell [1]. The first numerical evaluation of multiway data was reported by the same researcher and his wife Alberta, a mathematician by training, in 1955 [2], shortly after the introduction of the first programmable computer, the ILLIAC I. It remained silent in analytical chemistry for almost 25 years. When asked by me about the origins (during a postdoc period 1994–1996), the late Bruce Kowalski, a cofounder of the field of chemometrics but an analytical chemist by training, told the following story. Theoretical chemist Ernest Davidson had found, in collaboration with analytical chemists Chu-Ngi Ho and Gary Christian, a procedure for analyzing certain multiway data that enabled the determination of the analyte of interest in the presence of unsuspected interferents. Ernest Davidson plainly asked Bruce Kowalski: “Is this useful?” Bruce Kowalski immediately replied. “Yes, this is VERY useful!” That early work led to a series of three papers [3–5], and an improvement by Avraham Lorber [6]. Another landmark paper was published by Gene Sanchez and Bruce Kowalski in 1986 [7].1

What happened next? Of course, this development provoked a response by Svante Wold, organic chemist by training, leading chemometrician at the time and no doubt the father of the field of chemometrics, and therefore always in healthy competition with Bruce Kowalski's department. Paul Geladi explained to me during a stay at Wold's department in 1994 that they questioned the validation of the method developed in Seattle. The response came quickly [8,9] in the form of an addition to “their” favorite PLS for dealing with unsuspected interferents, now known as residual bilinearization. Interestingly, these two approaches are still among the main working horses to this very date!

The theoretical foundations were further disclosed by, among others, psychometrician Henk Kiers, Nicolas Sidiropoulos, who is highly active in Electrical and Computer Engineering, in collaboration with chemometrician Rasmus Bro and econometrician Age Smilde. Psychometrician Pieter Kroonenberg should not be left unmentioned here. And I very much appreciated the innovative work of statisticians Marie Linder and Rolf Sundberg on bilinear least squares. The algorithmic advances developed by physicist Pentti Paatero, who often collaborated with environmental scientist and chemometrician Phil Hopke, were also quite impressive and highly cited. (Of course, any omission here is a nonintended fault on my side.) And gradually, the number of applications started to boom, but notably so within chemometrics. One might say that it was the cross-fertilization between researchers from many seemingly unrelated fields that largely contributed to this topic becoming mainstream research throughout.

There is still one important article that I would like to pay attention to, written by mathematician Sue Leurgans and biochemist Robert Ross [10], which led one of the discussants, well-known psychometrician Jan de Leeuw, to exclaim in despair:

In a sense, the applicability of these models justifies the attention they have gotten so far. But from the mathematical and the statistical point of view, the available results are still very primitive. We have an elaborate notation (actually, several elaborate notations), in many cases featuring specially defined operators, that make multiway arrays look like ordinary linear operators. As the efforts of Rice, Hitchcock and Oldenburger have shown, it is difficult to distill beautiful results out of this orgy of subscripts and ad hoc notation. Either there is not enough structure there, or we have not found the key yet.

In my opinion, the pertinent methodology, as it is firmly founded in today's theory, has gradually moved quite far away from de Leeuw's sobering conclusion in 1992. A disclaimer is appropriate. Since I feel highly privileged and lucky to have worked with leading researchers on this topic, I should refer to this introduction as an opinion piece. Anyway, the reader always decides what to do with it!

To conclude, apart from promoting cross-fertilization between practical analytical chemists and chemometricians (or scientists with comparable skills), I take this opportunity to urge instrument developers to more closely look into this topic. That would constitute an immense leap ahead. As a first step, they should contemplate hiring chemometricians (or scientists with comparable skills), who show a keen awareness of the many barriers toward safely implementing this methodology in the instrument software; I mean full-time, not as mere consultants. As a major advantage, for example, better detection capabilities are in close reach, without additional experimentation, probably even less. Any chemometrician should feel motivated by the following visionary claim of Bruce Kowalski: “Chemometrics is only to have real impact when it is being built in commercial software.” I can therefore be very short about the future: much is still left to...

Produkt-Details

• Erscheint lt. Verlag: 17.8.2015
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik
• Themenwelt: Naturwissenschaften ► Chemie ► Analytische Chemie
• Themenwelt: Naturwissenschaften ► Chemie ► Physikalische Chemie
• Themenwelt: Technik
• ISBN-10: 0-444-63537-8 / 0444635378
• ISBN-13: 978-0-444-63537-2 / 9780444635372